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<b>let </b><font color="Maroon" title="c1">C1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C2</font>, <font color="Olive" title="b2">C3</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> <br/> for <font color="Olive" title="b3">F</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Olive" title="b1">C2</font><br/> for <font color="Olive" title="b4">G</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Olive" title="b1">C2</font>,<font color="Olive" title="b2">C3</font>  st <font color="Olive" title="b3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Olive" title="b4">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> holds <br/><font color="Olive" title="b4">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a></span><br/><b>let </b><font color="Maroon" title="c2">C2</font>, <font color="Maroon" title="c3">C3</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>  st <font color="Olive" title="b1">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Olive" title="b2">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> holds <br/><font color="Olive" title="b2">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a></span><br/><b>let </b><font color="Maroon" title="c4">F</font> be  <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>  st <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Olive" title="b1">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> holds <br/><font color="Olive" title="b1">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a></span><br/><b>let </b><font color="Maroon" title="c5">G</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> implies <font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> )</span><br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a></span><br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green" title="E12">A2</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> )
 
<b>by </b><i><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E3:16"/><i><font color="Green" title="E13">A3</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> &amp; <font color="Maroon" title="c5">G</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a> )
 
<b>by </b><i><a class="txt" href="functor1.html#E1:16"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E4:16"/><i><font color="Green" title="E14">A4</font></i>: 
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E2:16"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="functor1.html#T11" target="_self" title="FUNCTOR1:th.11">Th11</a></i>;<br/>
<a NAME="E5:16"/>
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E3:16"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="functor1.html#T12" target="_self" title="FUNCTOR1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E6:16"/>
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>by </b><i><a class="txt" href="functor1.html#E4:16"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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